I think Karen should respond to the requests with something like, "Thank you for the interest, but it would be inappropriate and unprofessional of me to select students to participate in my wedding." Because it's true.
Those parents have some nerve.
This, or "It would be unfair to pick one student when I care about them all, so I will not be having any students in my wedding party because I don't want any hurt feelings."
That leaves the door open for Karen to have a flower girl if she wants one, just not one of her students.
The resumes, the competition for the position--these mothers are a) making some interesting assumptions (that Karen will have a flower girl, that she wants students in her wedding) and b) very presumptuous. I'm just sort of stunned that there are flower girl resumes and that mothers would push so very hard for this. I could see a close friend or relation wanting their child in the wedding, but this is ridiculous.
On the other hand, Karen could wait a few more days, getting in more resumes and requests for "pick my daughter please!" and then announce that she will chose her flower girl from the pool of students who have not requested the privilege and have not turned in resumes. That would be a little bit mean, but it might teach some parents a lesson.